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Lower bounds for the extrinsic total curvatures of a space-like codimension 2 surface in Minkowski space. (English) Zbl 0703.53052

Given an orthogonal splitting of Minkowski space \(M^ 4=E^ 3\oplus E^-\) and a spacelike surface immersed in \(M^ 4\) two well-defined lightlike sections of the normal bundle of the surface can be defined. Using these sections two split curvatures and two split mean curvatures can be defined, and through these a quartic curvature K and a quartic mean curvature H. The author then proves several theorems involving the associated total curvatures for any oriented, compact surface.
Reviewer: M.Magid

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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